Piezoelectric materials: continuous-time and discrete-time dynamic models and control

In this paper two approximate linear time-invariant dynamic models, a continuous-time model and a discrete-time one, are proposed for a planar sandwich structure, constituted by two thin piezoelectric elements, mounted on a thin elastic support. The continuous-time model is determined by applying the integral Hamilton principle, once the kinematics of the structure has been approximated by a polynomial function; the discrete-time model is obtained via the direct discretization of the action functional. The non-interacting control and tracking of reference trajectories are stated and solved, both in the continuous-time case and in the discrete-time one. Some simulation results are reported in the paper